Derivational Complexity: TRS pair #487103466

details

property	value
status	complete
benchmark	26933.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	ICFP_2010

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	297.37 seconds
cpu usage	959.632
user time	952.903
system time	6.72837
max virtual memory	1.8784124E7
max residence set size	1.4985108E7

stage attributes

key	value
starexec-result	KILLED

output

KILLED
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 47 ms]
(4) CpxRelTRS
(5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
(6) CpxRelTRS
    (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (8) typed CpxTrs
    (9) OrderProof [LOWER BOUND(ID), 0 ms]
    (10) typed CpxTrs
(11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
(12) TRS for Loop Detection
(13) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
(14) CpxTRS
(15) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(16) CpxRelTRS
    (17) RcToIrcProof [BOTH BOUNDS(ID, ID), 1497 ms]
    (18) CpxRelTRS
    (19) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (20) CpxWeightedTrs
        (21) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 30 ms]
        (22) CpxWeightedTrs
        (23) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
        (24) CpxTypedWeightedTrs
        (25) CompletionProof [UPPER BOUND(ID), 0 ms]
        (26) CpxTypedWeightedCompleteTrs
            (27) NarrowingProof [BOTH BOUNDS(ID, ID), 2234 ms]
            (28) CpxTypedWeightedCompleteTrs
            (29) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 157 ms]
            (30) CpxRNTS
            (31) SimplificationProof [BOTH BOUNDS(ID, ID), 133 ms]
            (32) CpxRNTS
        (33) CompletionProof [UPPER BOUND(ID), 9 ms]
        (34) CpxTypedWeightedCompleteTrs
            (35) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 26 ms]
            (36) CpxRNTS
    (37) CpxTrsToCdtProof [UPPER BOUND(ID), 912 ms]
    (38) CdtProblem
        (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 3 ms]
        (40) CdtProblem
        (41) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (42) CdtProblem
        (43) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms]
        (44) CdtProblem
        (45) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 6657 ms]
        (46) CdtProblem
        (47) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1964 ms]
        (48) CdtProblem
        (49) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2023 ms]
        (50) CdtProblem
        (51) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 2028 ms]
        (52) CdtProblem
        (53) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1995 ms]
        (54) CdtProblem
        (55) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1877 ms]
        (56) CdtProblem
        (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 1810 ms]
        (58) CdtProblem
        (59) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4241 ms]
        (60) CdtProblem


----------------------------------------

(0)
Obligation:
The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(1, INF).


The TRS R consists of the following rules:

   0(0(1(2(3(3(1(x1))))))) -> 0(0(2(1(3(3(1(x1)))))))
   2(1(1(0(3(1(0(x1))))))) -> 2(0(1(1(3(1(0(x1)))))))
   1(3(2(0(0(4(1(4(0(x1))))))))) -> 1(3(2(0(1(0(4(4(0(x1)))))))))
   1(5(0(2(3(3(2(2(1(x1))))))))) -> 1(0(3(5(2(2(3(2(1(x1)))))))))
   2(5(2(1(5(4(2(4(0(x1))))))))) -> 2(5(2(5(1(4(2(4(0(x1)))))))))
   5(2(0(4(2(5(4(5(2(x1))))))))) -> 5(2(0(4(5(2(4(5(2(x1)))))))))
   0(3(2(4(3(2(2(0(4(2(x1)))))))))) -> 5(1(4(2(3(4(5(1(0(5(x1))))))))))
   3(0(4(3(0(1(4(4(4(2(x1)))))))))) -> 4(5(0(0(2(1(0(5(5(2(x1))))))))))
   0(0(4(4(0(0(3(4(5(4(2(x1))))))))))) -> 4(1(5(3(1(0(5(3(1(1(x1))))))))))
   0(1(4(4(3(1(1(1(2(2(4(x1))))))))))) -> 3(3(1(3(4(3(1(1(0(0(x1))))))))))
   0(2(3(4(1(5(5(0(0(1(1(x1))))))))))) -> 1(1(4(3(4(3(5(5(4(4(x1))))))))))
   0(3(0(4(3(3(3(0(5(3(4(x1))))))))))) -> 4(3(4(0(2(4(4(5(4(4(x1))))))))))
   0(3(1(4(0(0(2(2(4(4(0(x1))))))))))) -> 5(5(3(3(3(3(3(2(0(0(x1))))))))))
   0(3(3(0(5(5(5(2(2(3(4(x1))))))))))) -> 0(3(5(4(4(3(4(3(2(4(x1))))))))))
   0(4(3(5(3(3(5(4(0(0(4(x1))))))))))) -> 5(2(5(0(4(4(1(1(2(0(x1))))))))))
   0(4(4(1(1(1(2(0(2(4(0(x1))))))))))) -> 2(5(4(2(5(0(4(0(3(0(x1))))))))))
   1(0(0(5(5(5(4(5(4(3(3(x1))))))))))) -> 4(2(5(5(1(0(1(2(1(3(x1))))))))))
   1(0(5(0(3(5(3(1(2(2(0(x1))))))))))) -> 1(5(1(0(4(1(0(5(2(2(x1))))))))))
   2(1(1(0(1(3(1(4(0(1(4(x1))))))))))) -> 3(4(0(5(5(3(0(3(0(5(x1))))))))))
   2(1(1(4(0(5(0(1(2(4(2(x1))))))))))) -> 0(1(3(3(0(1(0(2(3(2(x1))))))))))
   2(1(4(0(2(2(1(2(4(2(0(x1))))))))))) -> 4(3(2(2(1(0(2(3(2(1(x1))))))))))

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Derivational Complexity: TRS